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Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials

Author

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  • Felipe Lara

    (Universidad de Tarapacá)

  • Rubén López

    (Universidad de Tarapacá)

Abstract

The q-asymptotic function is a new tool that permits to study nonconvex optimization problems with unbounded data. It is particularly useful when dealing with quasiconvex functions. In this paper, we obtain formulas for the q-asymptotic function via c-conjugates, directional derivatives and subdifferentials. We obtain them under lower semicontinuity or local Lipschitz assumptions. The well-known formulas for the asymptotic function in the convex case are consequences of these ones. We obtain a new formula for the convex case.

Suggested Citation

  • Felipe Lara & Rubén López, 2017. "Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 793-811, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1101-8
    DOI: 10.1007/s10957-017-1101-8
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    References listed on IDEAS

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    1. WEGGE, Leon L., 1974. "Mean value theorem for convex functions," LIDAM Reprints CORE 185, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Wegge, Leon L., 1974. "Mean value theorem for convex functions," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 207-208, August.
    3. Fabián Flores-Bazán & Fernando Flores-Bazán & Cristián Vera, 2015. "Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives," Journal of Global Optimization, Springer, vol. 63(1), pages 99-123, September.
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    Cited by:

    1. Alfredo Iusem & Felipe Lara, 2019. "Optimality Conditions for Vector Equilibrium Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 187-206, January.
    2. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.

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